Rewrite the Sum as a Rational Function S(n) $\sum _ { i = 1 } ^ { n } \frac { i ^ { 3 } } { n ^ { 3 } }$

Multiple Choice

Rewrite the sum as a rational function S(n) . $\sum _ { i = 1 } ^ { n } \frac { i ^ { 3 } } { n ^ { 3 } }$

A) $S ( n ) = \frac { n ^ { 2 } + 2 n + 1 } { 4 n ^ { 2 } }$
B) $S ( n ) = \frac { n ^ { 2 } + 2 n + 1 } { 4 n ^ { 4 } }$
C) $S ( n ) = \frac { n ^ { 2 } + 2 n + 1 } { 4 n ^ { 5 } }$
D) $S ( n ) = \frac { n ^ { 2 } + 2 n + 1 } { 4 n ^ { 3 } }$
E) $S ( n ) = \frac { n ^ { 2 } + 2 n + 1 } { 4 n }$